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A Benchmark Approach to Filtering in Finance

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  • Eckhard Platen

    ()

  • Wolfgang Runggaldier

Abstract

The paper proposes the use of the growth optimal portfolio for pricing and hedging in incomplete markets when there are unobserved factors that have to be filtered. The proposed filtering framework is applicable also in cases when there does not exist an equivalent risk neutral martingale measure. The reduction of the variance of derivative prices for increasing degrees of available information is measured. Copyright Springer Science + Business Media, Inc. 2004

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File URL: http://hdl.handle.net/10.1007/s10690-005-4301-4
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Bibliographic Info

Article provided by Springer in its journal Asia-Pacific Financial Markets.

Volume (Year): 11 (2004)
Issue (Month): 1 (March)
Pages: 79-105

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Handle: RePEc:kap:apfinm:v:11:y:2004:i:1:p:79-105

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Web page: http://springerlink.metapress.com/link.asp?id=102851

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Keywords: financial modeling; stochastic filtering; benchmark approach; growth optimal portfolio; fair pricing under partial information;

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References

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  1. Wolfgang Breymann & Leah Kelly & Eckhard Platen, 2005. "Intraday Empirical Analysis and Modeling of Diversified World Stock Indices," Asia-Pacific Financial Markets, Springer, vol. 12(1), pages 1-28, March.
  2. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer, vol. 11(1), pages 1-22, March.
  3. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
  4. N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
  5. P. Fischer & Eckhard Platen, 1999. "Applications of the Balanced Method to Stochastic Differential Equations in Filtering," Research Paper Series 16, Quantitative Finance Research Centre, University of Technology, Sydney.
  6. David Heath & Eckhard Platen, 2002. "Consistent Pricing and Hedging for a Modified Constant Elasticity of Variance Model," Research Paper Series 78, Quantitative Finance Research Centre, University of Technology, Sydney.
  7. Bhar Ramaprasad & Chiarella Carl & Runggaldier Wolfgang J., 2004. "Inferring the Forward Looking Equity Risk Premium from Derivative Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(1), pages 1-26, March.
  8. Eckhard Platen & Gerhard Stahl, 2003. "A Structure for General and Specific Market Risk," Research Paper Series 91, Quantitative Finance Research Centre, University of Technology, Sydney.
  9. Eckhard Platen, 2002. "Benchmark Model with Intensity Based Jumps," Research Paper Series 81, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. Robert J. Elliott & John van der Hoek, 1997. "An application of hidden Markov models to asset allocation problems (*)," Finance and Stochastics, Springer, vol. 1(3), pages 229-238.
  11. I. Bajeux-Besnainou & R. Portait, 1997. "The numeraire portfolio: a new perspective on financial theory," The European Journal of Finance, Taylor & Francis Journals, vol. 3(4), pages 291-309.
  12. Eckhard Platen, 2003. "A Benchmark Framework for Risk Management," Research Paper Series 113, Quantitative Finance Research Centre, University of Technology, Sydney.
  13. Long, John Jr., 1990. "The numeraire portfolio," Journal of Financial Economics, Elsevier, vol. 26(1), pages 29-69, July.
  14. Ram Bhar & Carl Chiarella & Wolfgang Runggaldier, 2001. "Estimation in Models of the Instantaneous Short Term Interest Rate By Use of a Dynamic Bayesian Algorithm," Research Paper Series 68, Quantitative Finance Research Centre, University of Technology, Sydney.
  15. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
  16. Carl Chiarella & Sara Pasquali & Wolfgang Runggaldier, 2001. "On Filtering in Markovian Term Structure Models (An Approximation Approach)," Research Paper Series 65, Quantitative Finance Research Centre, University of Technology, Sydney.
  17. Ram Bhar & Carl Chiarella & Wolfgang Runggaldier, 2001. "Filtering Equity Risk Premia From Derivative Prices," Research Paper Series 69, Quantitative Finance Research Centre, University of Technology, Sydney.
  18. R. Elliott & Eckhard Platen, 1999. "Hidden Markov Chain Filtering for Generalised Bessel Processes," Research Paper Series 23, Quantitative Finance Research Centre, University of Technology, Sydney.
  19. Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series 103, Quantitative Finance Research Centre, University of Technology, Sydney.
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Citations

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Cited by:
  1. Claudio Fontana & Wolfgang J. Runggaldier, 2012. "Diffusion-based models for financial markets without martingale measures," Papers 1209.4449, arXiv.org, revised Feb 2013.
  2. Eckhard Platen & Wolfgang Runggaldier, 2007. "A Benchmark Approach to Portfolio Optimization under Partial Information," Research Paper Series 191, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Ke Du & Eckhard Platen, 2011. "Three-Benchmarked Risk Minimization for Jump Diffusion Markets," Research Paper Series 296, Quantitative Finance Research Centre, University of Technology, Sydney.

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